# Current capacity of multi-strand versus single-strand

Discussion in 'Electronic Basics' started by Zarbol Tsar, Dec 3, 2004.

1. ### Zarbol TsarGuest

Would a multi-strand flexible wire have the same current carrying
capacity as a solid single stranded cable of the same cross section.

For example ... a multi-strand with a cross section for its wire
portion of 0.75 mm squared and a single strand cable also of 0.75 mm
squared.

2. ### Palindrâ˜»meGuest

Any particular frequency in mind?

Skin effect is the obvious thing that will make a stranded wire better
than a solid of the same csa. But this kicks in at higher frequencies.

Here is a brief simplified guide:

http://www.st-andrews.ac.uk/~www_pa/Scots_Guide/audio/skineffect/page1.html

However, if the actual csa of the solid wire is compared with actual csa
of the stranded wire (rather than the sum of the csa of individual
strands), then a solid wire will have more copper and hence lower
resistance. This is frequency independent.

So, at low frequencies or DC, a solid wire of the same core diameter
will be better than stranded. As frequency rises, a point will come
where stranded wire will be better; it will be able to take a higher
current than a solid core of the same diameter.

There are obviously exceptions.

Hope that is what you were after...

3. ### Tim WilliamsGuest

Ya, until you get into higher frequencies where the slightly greater surface
area of the stranded wire represents more cross section. Probably above
10MHz...

Tim

4. ### Andrew GabrielGuest

Skin effect is easily measurable at a few tens of kHz.
It comes into effect at regular mains frequences for very large
conductors. An alternative to making them stranded is to pick
a different shape which avoids significant depth of metal,
such as a flat strip (thin rectangular profile), or tubular.

5. ### John PopelishGuest

In most cases, they are exactly the same. When the frequency gets
high enough that skin effect starts to crowd the current toward the
surface, stranded wire has a slight advantage, but this is greatly
enhanced if all the strands are insulated from each other (look up
litz wire). This effect can also be used ot advantage when winding
magnetic devices with enameled wire, and two or more parallel strands
can be used in place of an equivalent cross section single wire. But
for ordinary hook up wire, they are usually assumed to have an
ampacity based on their cross sectional area, not the number of
strands.

6. ### Gerald Newton3Guest

A No, 12 AWG wire has a diameter of 0.78 mm.

For wire sizes 2.47 mm and under (No. 2 AWG and under) the DC resistance
nearly equals AC resistance. Therefore the ampacity for stranded conductors
is nearly equal to that for solid conductors for these small conductors
(also demonstrated using the N-M equations.) For building wire types,
conductors size No. 8 AWG and larger that are installed in raceways are
required to be stranded (NEC Section 310.3.) Therefore, we seldom see
conductors larger than No. 8 that are solid, except for the No. 4 bare
grounding conductors carried on line trucks and sold for services by supply
houses that are used as grounding electrode conductors so that no additional
protection is required. The standard ampacity table in the NEC used for
building wires, 310.16, does not distinguish between solid and stranded
conductors. This is probably because almost all building wire No. 8 and
larger is stranded.
The N-M equations also do not distinguish between solid and stranded, but
uses DC resistance multiplied by (1+YC) where YC becomes measurable for
wire sizes above No. 2 because of skin effect.

7. ### Gerald Newton3Guest

For No. 12 AWG Table 8 of the NEC does list two different DC resistances for
stranded and solid copper.

DC resistance per 1000 feet for solid is 1.93 ohms

For stranded the DC resistance is given as 1.98 ohms per 1000 feet.

So solid should have a slightly higher ampacity.

If we use Table 310.16 of the NEC to determine RCA and substitute into the
Ampere calculation we can find the approximate differences in ampacity.

From Table 310.16 using 75 degrees C as the ambient.

I = 25 amperes, TC = 75 degrees C, and TA = 30 degrees C and RDC = 1.98 ohms
per 1000 feet or 0.00198 ohms per foot.

This converts to 1980 microhms.

From I (in kiloamperes) = SQRT(( TC-TA)/RDC*RCA))

Or

RCA=(TC-TA)/RDC*I*I

Or RCA = (75-30)/1980*0.025*0.025

RCA = 36 thermal ohm feet

For stranded, I = 0.025 kiloamperes from the table

For solid No. 12 copper

I (in kiloamperes) = SQRT ((75-30)/1930*36)

or I = 0.0254 kiloamperes

Then the solid No. 12 copper would have a 0 .4 ampere increase in ampacity.

This is a 0.4/25 *100 or only a 1.6 per cent increase.

Considering that ampacity tables are approximations, this increase in
ampacity does not exceed the error of approximation.

8. ### Tom BiasiGuest

If indeed the conducting areas are the same the capacity will be the same
for all practical purposes.
The AWG (American Wire Gauge) numbers take into account the actual total
cross-sectional area.
Some charts will compare stranded vs. solid for actual wire outer diameter
though.
If you start talking about impedance in some applications the story will
change.
Regards,
Tom

9. ### RowbotthGuest

As far as I am aware, the amount of copper being the same should mean
the same current flow - but the more strands should mean it is easier to
work with, albeit more expensive?

H.

10. ### Gerald Newton3Guest

I just reviewed the Samuel Rosch Paper from 1938, "The Current Carrying
Capacity of Rubber-Insulated Conductors."
He used a slightly different formula where N represented the number of
current carrying conductors. Since Table 310.16 is for three current
carrying conductors in a raceway to find RCA the following should be used:

I (in kiloamperes) = SQRT(( TC-TA)/N*RDC*RCA))
RCA=(TC-TA)/N*RDC*I*I
RCA = (75-30)/3*1980*0.025*0.025
RCA= 12 Thermal Ohm Feet

Then for solid No. 12 AWG copper:
I (in kiloamperes) = SQRT ((75-30)/3*1930*12)
I = 0.0254 kiloamperes

And there is no difference in the answer.

11. ### Gerald Newton3Guest

I should also note that Samuel Rosch did his calculation for an ambient of
30 degrees C and TC = 50 degrees.
He came up with the following ampacity table for copper (only sizes up to
No. 2 are shown):

Wire Size - Amperes
14 - 15
12 - 19
10 - 26
8 - 35
6 - 47
4 - 61
2 - 78
To convert these values to ampaeres for a TC (insulation temperature) equal
to 75 degrees C. We need to derive an equation:
Let I1 equal ampacity for 50 degree insulation and I2 equal ampacity for 75
degree insulation,
Then:
I1 (in kiloamperes) = SQRT(( TC1-TA)/N*RDC1*RCA))
I2 (in kiloamperes) = SQRT(( TC2-TA)/N*RDC2*RCA))
Where TA = 30 degrees C.
and RCA is equal in both equations.
RDC1 is DC resistance in microhms at 50 degrees C
RDC2 is DC resistance in microhms at 75 degrees C.
TC1 = 50 degrees C.
TC2 = 75 degrees C.
Using the proportionality rule where two ratios that are equal can be cross
multiplied:
I2*(SQRT(( TC1-TA)/N*RDC1*RCA))) = I1*(SQRT(( TC2-TA)/N*RDC2*RCA)))
and squaring both sides:
I2*I2*(( TC1-TA)/N*RDC1*RCA)) = I1*I1*(( TC2-TA)/N*RDC2*RCA))
I2*I2 = (I1*I1*(( TC2-TA)/N*RDC2*RCA))) / (( TC1-TA)/N*RDC1*RCA))
I2*I2 = I1*I1*( TC2-TA) * RDC1/ ( TC1-TA) * RDC2
I2 = I1* SQRT (( TC2-TA) * RDC1 / ( TC1-TA) * RDC2)

Next we use the N-M equation for finding DC resistance:

rdc = ohms
pc = circular mil ohms per foot of conductor at 20 degrees C. (10.371 ohms
for 100% IACS copper, 17.002 ohms for 61% IACS aluminum)
tah = absolute value of inferred temperature of zero resistance. (234.5
degrees C. for copper and 228.1 degrees C. for aluminum)
cma = circular mil area of conductor from Chapter 9 Table 8 of NEC
tc = conductor temperature in degrees C.

At 50 degrees C.
RDC1 = (1.02 * 10.371 / CMA) * (234.5 + 50) / (234.5 + 20)
At 75 degrees C.
RDC2=(1.02 * 10.371 / CMA) * (234.5 + 75) / (234.5 + 20)

If we feed this into a spreadsheet we come up with the following ampacity
table for TC = 75 degrees C.
We get the following table:
Wire size - amperes
14 - 21
12 - 27
10 - 37
8 - 50
6 - 67
4 - 88
2 - 112
If we round these to the nearest 5 amperes:
14 - 20
12 - 25
10 - 35
8 - 50
6 - 65
4 - 90
2 - 110
How do these compare to table 310.16?
wire size - calculated amperes - Table 310.16

14 - 20 - 20
12 - 25 - 25
10 - 35 - 35
8 - 50 - 50
6 - 65 - 65
4 - 90 - 85
2 - 110 - 115

This shows that Table 310.16 in the NEC has a general round off error that
exceeds the difference in ampacities between solid and stranded conductors
(at 60 Hz) for small wire sizes.

12. ### Dimitrios TzortzakakisGuest

In very high voltages, 400 kV and over, it's not the same due to corona
effect (ionization of the air around the conductor).So, the utility puts two
conductors in parallel.That's the only example I can think of;in every day
applications it has no meaning.

13. ### Dimitrios TzortzakakisGuest

What I mentioned before, is actually the strength of the electric field
around the conductor, that is reduced by the use of two (conductors) and
ionizes the air, making a noise like humming bees.

14. ### Dimitrios TzortzakakisGuest

Here, we use the following gauges (in residence and small industry):1.5,
2.5, 4, 6, 10 mm^2.The former 3 are stranded or solid, the latter 2 always
stranded.It's very difficult to bend the thick wires when they are solid, so
they stopped producing solid 10 mm^2 wires, used to wire old-fashioned fuses
and circuit breakers.The ampacity of these conductors is 10,16,20,25,35
amperes respectively and should be properly fused, according to local rules,
with circuit breakers.Actually, the max.current of a copper wire depends on
the max.allowed temperature, hence whether the insulation is PVC or
something else (usually PVC here).All formulas have the gauge in mm^2 here,
my book says nothing about the mentioned issue, maybe it's different in USA.
the voltage drop in a (loaded) cable is:
ÄU/U=2 I Ø' I cos ö /U
(the greek letters are delta, psi and phi respectively)

15. ### Gerald Newton3Guest

Are your areas the total area of stranded or solid or are they the combined
area of the copper only.
We use Circular Mil Area (CMA) to define the copper area.

CMA is the diameter of a conductor in thousandths of an inch squared and
represents the total copper area.
For instance, a No. 12 AWG has a CMA equal to 6530 for both stranded and
solid No. 12 conductors, but the cross sectional areas are different.
The cross sectional area of a solid No. 12 is 3.31 MM^2 and 4.25 mm^2 for
stranded. Cross sectional areas do little for calculating ampacity.
We use CMA because resistance is inversely proportional to CMA because CMA
represents actual copper.
Also you give your ampacities, but what maximum operating temperature are
these for and what is the ambient temperature?
Also, are your ampacities for in cable, 3 conductors in raceway, etc.

16. ### Don KellyGuest

------------------------
Utilities use bundled conductors at lower that 400KV. The main reasons for
this is to
a)make construction easier and cheaper
b)reduce the series inductance of the line
c) reduce conductor surface fields and corona.
So you have hit one reason out of three.

17. ### Dimitrios TzortzakakisGuest

That means I am not passing the exam?

18. ### Dimitrios TzortzakakisGuest

The ampacities are for normal conditions, thus residence.It's a thumb rule
which cable to use for what load.A cooking range needs 6 mm^2, a water
heater 4 mm^2, a washing machine and dishwasher and most space heaters 2.5
mm^2 and incadescent lighting 1.5 mm^2.I suppose these calculations are for
the climate of Greece, and for three wires (live, neutral, earth) in a
conduit.

19. ### Andrew GabrielGuest

Area of the copper only, in Europe.

Assumes ambient of 30ºC and maximum operating temperature of 70ºC.
For ambient temperatures above 30ºC, max current is reduced by
tables, and reaches zero at 70ºC. Circuit protection for overload
and fault current conditions is designed to prevent cable exceeding
160ºC during a fault or overload (i.e. a maximum 90ºC temperature
rise from operating temperature), or it would be permanantly
damaged and need replacing. Higher temperature cable is available
for situations which require it.
We have different maximum ampacities for a number of different
installation methods. The highest is for a cable in a cable tray,
going through to the lowest which is for a cable embedded in a
thermally insulating wall. We also have 'grouping factor' which
reduces the ratings of multiple cables when closely spaced.

20. ### Gerald Newton3Guest

"Normal conditions" is a broad term. In the USA the NEC (National
Electrical Code) has many specifics for ampacity tables. For instance, the
main Table 310.16 that we use for building wire ampacity defines the ambient
as 30 degrees C. and has derating factors where the temperature exceeds this
for long runs. If the temperature is excessive for no more than 10 per cent
of the circuit length to a maximum of ten feet whichever is less, then no
excessive temperature derating is required. The ampacities are also defined
for no more than three current carrying conductors in a raceway or cable.
If conductors are bundled or cables with more than three current carrying
conductors are bundled for longer than 24 inches or if there are more than
three current carrying conductors in a raceway or cable there are additional
derating factors. In some cases where there is excessive temperatures and
more than three current carrying conductors double derating is required. We
also have a rule for continuous loads requiring a 80 per cent derating.
There are also rules defining a current carrying conductor. If a neutral
only carries unbalanced current it is not counted as a current carrying
conductor. But where the majority of current in a neutral is from discharge
lighting, third harmonics, or computer loads it is counted. Also, the
grounding conductor is not counted as a current carrying conductor. Also,
ampacities are listed for three temperatures for copper and for aluminum.
One column is for 60 degrees insulation, one for 75 degrees C. and one
column for 90 degree C. The maximum operating temperature of a conductor
cannot exceed the maximum allowed rated operating temperature for the
terminals, equipment or insulation whichever is the lesser. We can use the
90 degree column for derating purposes. For example if there are 9 No. 12
AWG (American Wire Gauge) 90 degree C. rated current carrying conductors in
a raceway we can multiply the derating factor of .7 times the 90 degree
ampacity of 30 amperes to get 21 amperes and use this as the ampacity but
other rules still apply. Our rules are so complicated that it took me about
5 weeks to write an Excel program to determine ampacity. This program is
accessible at http://www.electrician.com/calculators/T310-16.xls
But in general for dwelling units (where people live, eat, sanitize, and
sleep), we use No. 8 AWG copper on a two pole 40 ampere circuit breaker for
ranges, No. 10 AWG copper on a two pole 30 ampere circuit breaker for hot
water heaters, and No. 12 AWG copper on single pole 20 ampere circuit
breakers for general purpose lighting and appliance circuits.
The NFPA (National Fire Protection Association) that writes the NEC wants
the international community to adopt the NEC as an International Electrical
Code!
So you too may become acquainted with our famous NEC someday!